M2 Optimization

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Optimization is at the confluence of mathematics, computer science and economics, and its importance is growing both in academia and in industry. The Optimization master program deals with all components of mathematical optimization understood in the broadest sense, with a particular focus on those specific to Paris-Saclay, which is strenghtened by the presence of the Gaspard Monge Program for Optimization (PGMO). The themes include: optimal control (discrete and continuous time, deterministic and stochastic), game theory (theory, modeling in economics and networks), calculus of variations (and more generally optimization in analysis and PDE), stochastic optimization and stochastic methods for optimization, operation research. A significant part of the courses are shared with other programs and specialties in mathematics, computer science and economics.

Course Prerequisites

M1-level in mathematics or applied mathematics.

  • Understand and mathematically model a problem in order to resolve it.

  • Clearly explain a theory and mathematical results.

  • Be proficient in the use of digital tools and major programming languages.

  • Analyse a research paper with a view to summarising it and using it.

  • Analyse data and implement digital simulations.

  • Understand and proficiently use high-level mathematical tools and methods.

Post-graduate profile

The programme aims to prepare graduates to deal with the matters that arise in the applied sciences surrounding optimisation, optimal control and game theory: the mathematical modeling of a problem in terms of minimisation, maximisation or equilibrium, its mathematical analysis (existence, uniqueness, etc.), algorithmic approaches to determine such a problem or tackle it, and the effective implementation of those methods. Students are not necessarily expected to have a perfect command of all these aspects, since that depends on their previous studies and their chosen path: but they are expected to know how to position themselves faced with such problems, and they should have advanced experience in at least one.

Career prospects

Most students go on to do a thesis at the end of the programme, often in connection with a company (CIFRE industry contract or other contract). A minority enter working life at the end of the Master's.


Laboratoire de mathématiques d'Orsay
Laboratoire des Signaux et Systèmes.

Centre de Mathématiques Appliquées (Ecole Polytechnique)
Unité de Mathématiques Appliquées (ENSTA)
Fédération de Mathématiques (CentraleSupélec).


Les étudiants doivent suivre des cours parmi la liste ci-dessous.

Matières ECTS Cours TD TP Cours-TD Cours-TP TD-TP A distance Projet Tutorat
Théorie des jeux avancée et applications 5 30
Théorie des Jeux 5 30
Théorie de la complexité 3 20
Programmation Mathématique 5 30
Programmation dynamique 5 30
Optimisation stochastique 5 30
Optimisation sans gradient 5 30
Optimisation dans les Graphes 5 30
Optimisation continue avancée I 5 30
Jeux dynamiques à somme nulle 5 30
Introduction à la RO et la combinatoire 5 30
Contrôle des EDO 5 30
Calcul des variations 3 18
Apprentissage et optimisation séquentielle 4 20
Analyse et optimisation convexe 5 30

Les étudiants doivent valider 9 ECTS de cours et un stage ou un mémoire pour 21 ECTS.

Matières ECTS Cours TD TP Cours-TD Cours-TP TD-TP A distance Projet Tutorat
Transport optimal 3 18
Optimisation et statistique 4 20
Optimisation continue avancée II 3 18
Français Langue étrangère 2 24
Dynamique de l'information et de la communication dans les jeux 3 18
Cours invité PGMO 2 10
Contrôle géométrique 3 18
Contrôle des EDP 3 18
Compte-rendus de séminaires d'optimisation 2 15
Matières ECTS Cours TD TP Cours-TD Cours-TP TD-TP A distance Projet Tutorat
Stage ou Mémoire 21 0
Modalités de candidatures
Application period
From 01/03/2021 to 30/08/2021
Compulsory supporting documents
  • All transcripts of the years / semesters validated since the high school diploma at the date of application.

  • Curriculum Vitae.

  • Motivation letter.

Additional supporting documents
  • Curriculum EU (description of the units of education followed) of the last two years.

  • Choice sheet of M2 (obligatory for the candidates registered in M1 at the University Paris-Saclay) to download on https://www.universite-paris-saclay.fr/en/admission/apply-master-programmes.

  • Supporting documents (TOEFL, TOEIC, certificate of a teacher ...) of a level of a foreign language.

  • VAP file (obligatory for all persons requesting a valuation of the assets to enter the diploma).

Course manager(s)
Administrative office